Properties

Label 1950.2.y.b.49.2
Level $1950$
Weight $2$
Character 1950.49
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.b.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.366025 - 0.633975i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.366025 - 0.633975i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.09808 + 2.36603i) q^{11} +1.00000i q^{12} +(-2.50000 + 2.59808i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.96410 + 1.13397i) q^{17} -1.00000 q^{18} +(1.09808 + 0.633975i) q^{19} -0.732051i q^{21} +(4.09808 + 2.36603i) q^{22} +(5.36603 - 3.09808i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(0.366025 + 0.633975i) q^{28} +(1.23205 + 2.13397i) q^{29} -5.46410i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -2.26795i q^{34} +(0.500000 + 0.866025i) q^{36} +(5.23205 + 9.06218i) q^{37} -1.26795i q^{38} +(-0.866025 + 3.50000i) q^{39} +(9.86603 - 5.69615i) q^{41} +(-0.633975 + 0.366025i) q^{42} +(6.63397 + 3.83013i) q^{43} -4.73205i q^{44} +(-5.36603 - 3.09808i) q^{46} +8.19615 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.23205 + 5.59808i) q^{49} +2.26795 q^{51} +(-1.00000 - 3.46410i) q^{52} +0.464102i q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.366025 - 0.633975i) q^{56} +1.26795 q^{57} +(1.23205 - 2.13397i) q^{58} +(-6.92820 - 4.00000i) q^{59} +(-0.598076 + 1.03590i) q^{61} +(-4.73205 + 2.73205i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.56218 + 9.63397i) q^{67} +(-1.96410 + 1.13397i) q^{68} +(3.09808 - 5.36603i) q^{69} +(-1.09808 - 0.633975i) q^{71} +(0.500000 - 0.866025i) q^{72} -9.73205 q^{73} +(5.23205 - 9.06218i) q^{74} +(-1.09808 + 0.633975i) q^{76} +3.46410i q^{77} +(3.46410 - 1.00000i) q^{78} +9.46410 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-9.86603 - 5.69615i) q^{82} -10.1962 q^{83} +(0.633975 + 0.366025i) q^{84} -7.66025i q^{86} +(2.13397 + 1.23205i) q^{87} +(-4.09808 + 2.36603i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(0.732051 + 2.53590i) q^{91} +6.19615i q^{92} +(-2.73205 - 4.73205i) q^{93} +(-4.09808 - 7.09808i) q^{94} +1.00000i q^{96} +(3.00000 - 5.19615i) q^{97} +(3.23205 - 5.59808i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{11} - 10 q^{13} + 4 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 6 q^{22} + 18 q^{23} + 14 q^{26} - 2 q^{28} - 2 q^{29} - 2 q^{32} - 6 q^{33} + 2 q^{36} + 14 q^{37} + 36 q^{41} - 6 q^{42} + 30 q^{43} - 18 q^{46} + 12 q^{47} + 6 q^{49} + 16 q^{51} - 4 q^{52} - 2 q^{56} + 12 q^{57} - 2 q^{58} + 8 q^{61} - 12 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 6 q^{68} + 2 q^{69} + 6 q^{71} + 2 q^{72} - 32 q^{73} + 14 q^{74} + 6 q^{76} + 24 q^{79} - 2 q^{81} - 36 q^{82} - 20 q^{83} + 6 q^{84} + 12 q^{87} - 6 q^{88} + 12 q^{89} - 4 q^{91} - 4 q^{93} - 6 q^{94} + 12 q^{97} + 6 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 0.366025 0.633975i 0.138345 0.239620i −0.788526 0.615002i \(-0.789155\pi\)
0.926870 + 0.375382i \(0.122489\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) −4.09808 + 2.36603i −1.23562 + 0.713384i −0.968195 0.250196i \(-0.919505\pi\)
−0.267421 + 0.963580i \(0.586172\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) −0.732051 −0.195649
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.96410 + 1.13397i 0.476365 + 0.275029i 0.718900 0.695113i \(-0.244646\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.09808 + 0.633975i 0.251916 + 0.145444i 0.620641 0.784095i \(-0.286872\pi\)
−0.368725 + 0.929538i \(0.620206\pi\)
\(20\) 0 0
\(21\) 0.732051i 0.159747i
\(22\) 4.09808 + 2.36603i 0.873713 + 0.504438i
\(23\) 5.36603 3.09808i 1.11889 0.645994i 0.177775 0.984071i \(-0.443110\pi\)
0.941118 + 0.338078i \(0.109777\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) 3.50000 + 0.866025i 0.686406 + 0.169842i
\(27\) 1.00000i 0.192450i
\(28\) 0.366025 + 0.633975i 0.0691723 + 0.119810i
\(29\) 1.23205 + 2.13397i 0.228786 + 0.396269i 0.957449 0.288604i \(-0.0931910\pi\)
−0.728663 + 0.684873i \(0.759858\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i −0.871334 0.490691i \(-0.836744\pi\)
0.871334 0.490691i \(-0.163256\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.36603 + 4.09808i −0.411872 + 0.713384i
\(34\) 2.26795i 0.388950i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 5.23205 + 9.06218i 0.860144 + 1.48981i 0.871789 + 0.489881i \(0.162960\pi\)
−0.0116456 + 0.999932i \(0.503707\pi\)
\(38\) 1.26795i 0.205689i
\(39\) −0.866025 + 3.50000i −0.138675 + 0.560449i
\(40\) 0 0
\(41\) 9.86603 5.69615i 1.54081 0.889590i 0.542027 0.840361i \(-0.317657\pi\)
0.998788 0.0492283i \(-0.0156762\pi\)
\(42\) −0.633975 + 0.366025i −0.0978244 + 0.0564789i
\(43\) 6.63397 + 3.83013i 1.01167 + 0.584089i 0.911681 0.410899i \(-0.134785\pi\)
0.0999910 + 0.994988i \(0.468119\pi\)
\(44\) 4.73205i 0.713384i
\(45\) 0 0
\(46\) −5.36603 3.09808i −0.791177 0.456786i
\(47\) 8.19615 1.19553 0.597766 0.801671i \(-0.296055\pi\)
0.597766 + 0.801671i \(0.296055\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) 3.23205 + 5.59808i 0.461722 + 0.799725i
\(50\) 0 0
\(51\) 2.26795 0.317576
\(52\) −1.00000 3.46410i −0.138675 0.480384i
\(53\) 0.464102i 0.0637493i 0.999492 + 0.0318746i \(0.0101477\pi\)
−0.999492 + 0.0318746i \(0.989852\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 0.366025 0.633975i 0.0489122 0.0847184i
\(57\) 1.26795 0.167944
\(58\) 1.23205 2.13397i 0.161776 0.280205i
\(59\) −6.92820 4.00000i −0.901975 0.520756i −0.0241347 0.999709i \(-0.507683\pi\)
−0.877841 + 0.478953i \(0.841016\pi\)
\(60\) 0 0
\(61\) −0.598076 + 1.03590i −0.0765758 + 0.132633i −0.901770 0.432215i \(-0.857732\pi\)
0.825195 + 0.564848i \(0.191065\pi\)
\(62\) −4.73205 + 2.73205i −0.600971 + 0.346971i
\(63\) −0.366025 0.633975i −0.0461149 0.0798733i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.73205 0.582475
\(67\) 5.56218 + 9.63397i 0.679528 + 1.17698i 0.975123 + 0.221664i \(0.0711488\pi\)
−0.295595 + 0.955313i \(0.595518\pi\)
\(68\) −1.96410 + 1.13397i −0.238182 + 0.137515i
\(69\) 3.09808 5.36603i 0.372965 0.645994i
\(70\) 0 0
\(71\) −1.09808 0.633975i −0.130318 0.0752389i 0.433424 0.901190i \(-0.357305\pi\)
−0.563742 + 0.825951i \(0.690639\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −9.73205 −1.13905 −0.569525 0.821974i \(-0.692873\pi\)
−0.569525 + 0.821974i \(0.692873\pi\)
\(74\) 5.23205 9.06218i 0.608214 1.05346i
\(75\) 0 0
\(76\) −1.09808 + 0.633975i −0.125958 + 0.0727219i
\(77\) 3.46410i 0.394771i
\(78\) 3.46410 1.00000i 0.392232 0.113228i
\(79\) 9.46410 1.06479 0.532397 0.846495i \(-0.321291\pi\)
0.532397 + 0.846495i \(0.321291\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −9.86603 5.69615i −1.08952 0.629035i
\(83\) −10.1962 −1.11917 −0.559587 0.828772i \(-0.689040\pi\)
−0.559587 + 0.828772i \(0.689040\pi\)
\(84\) 0.633975 + 0.366025i 0.0691723 + 0.0399366i
\(85\) 0 0
\(86\) 7.66025i 0.826026i
\(87\) 2.13397 + 1.23205i 0.228786 + 0.132090i
\(88\) −4.09808 + 2.36603i −0.436856 + 0.252219i
\(89\) −2.19615 + 1.26795i −0.232792 + 0.134402i −0.611859 0.790967i \(-0.709578\pi\)
0.379068 + 0.925369i \(0.376245\pi\)
\(90\) 0 0
\(91\) 0.732051 + 2.53590i 0.0767398 + 0.265834i
\(92\) 6.19615i 0.645994i
\(93\) −2.73205 4.73205i −0.283300 0.490691i
\(94\) −4.09808 7.09808i −0.422684 0.732111i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 3.00000 5.19615i 0.304604 0.527589i −0.672569 0.740034i \(-0.734809\pi\)
0.977173 + 0.212445i \(0.0681426\pi\)
\(98\) 3.23205 5.59808i 0.326486 0.565491i
\(99\) 4.73205i 0.475589i
\(100\) 0 0
\(101\) −5.96410 10.3301i −0.593450 1.02789i −0.993764 0.111508i \(-0.964432\pi\)
0.400313 0.916378i \(-0.368901\pi\)
\(102\) −1.13397 1.96410i −0.112280 0.194475i
\(103\) 18.7321i 1.84572i 0.385131 + 0.922862i \(0.374156\pi\)
−0.385131 + 0.922862i \(0.625844\pi\)
\(104\) −2.50000 + 2.59808i −0.245145 + 0.254762i
\(105\) 0 0
\(106\) 0.401924 0.232051i 0.0390383 0.0225388i
\(107\) 0.169873 0.0980762i 0.0164222 0.00948139i −0.491766 0.870727i \(-0.663649\pi\)
0.508189 + 0.861246i \(0.330315\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 5.46410i 0.523366i 0.965154 + 0.261683i \(0.0842775\pi\)
−0.965154 + 0.261683i \(0.915723\pi\)
\(110\) 0 0
\(111\) 9.06218 + 5.23205i 0.860144 + 0.496604i
\(112\) −0.732051 −0.0691723
\(113\) 16.1603 + 9.33013i 1.52023 + 0.877705i 0.999716 + 0.0238510i \(0.00759271\pi\)
0.520513 + 0.853854i \(0.325741\pi\)
\(114\) −0.633975 1.09808i −0.0593772 0.102844i
\(115\) 0 0
\(116\) −2.46410 −0.228786
\(117\) 1.00000 + 3.46410i 0.0924500 + 0.320256i
\(118\) 8.00000i 0.736460i
\(119\) 1.43782 0.830127i 0.131805 0.0760976i
\(120\) 0 0
\(121\) 5.69615 9.86603i 0.517832 0.896911i
\(122\) 1.19615 0.108295
\(123\) 5.69615 9.86603i 0.513605 0.889590i
\(124\) 4.73205 + 2.73205i 0.424951 + 0.245345i
\(125\) 0 0
\(126\) −0.366025 + 0.633975i −0.0326081 + 0.0564789i
\(127\) 15.4641 8.92820i 1.37222 0.792250i 0.381010 0.924571i \(-0.375576\pi\)
0.991207 + 0.132321i \(0.0422429\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 7.66025 0.674448
\(130\) 0 0
\(131\) 13.4641 1.17636 0.588182 0.808729i \(-0.299844\pi\)
0.588182 + 0.808729i \(0.299844\pi\)
\(132\) −2.36603 4.09808i −0.205936 0.356692i
\(133\) 0.803848 0.464102i 0.0697024 0.0402427i
\(134\) 5.56218 9.63397i 0.480499 0.832249i
\(135\) 0 0
\(136\) 1.96410 + 1.13397i 0.168420 + 0.0972375i
\(137\) −0.964102 + 1.66987i −0.0823688 + 0.142667i −0.904267 0.426968i \(-0.859582\pi\)
0.821898 + 0.569634i \(0.192915\pi\)
\(138\) −6.19615 −0.527452
\(139\) −4.92820 + 8.53590i −0.418005 + 0.724005i −0.995739 0.0922197i \(-0.970604\pi\)
0.577734 + 0.816225i \(0.303937\pi\)
\(140\) 0 0
\(141\) 7.09808 4.09808i 0.597766 0.345120i
\(142\) 1.26795i 0.106404i
\(143\) 4.09808 16.5622i 0.342698 1.38500i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 4.86603 + 8.42820i 0.402715 + 0.697523i
\(147\) 5.59808 + 3.23205i 0.461722 + 0.266575i
\(148\) −10.4641 −0.860144
\(149\) 2.42820 + 1.40192i 0.198926 + 0.114850i 0.596154 0.802870i \(-0.296695\pi\)
−0.397228 + 0.917720i \(0.630028\pi\)
\(150\) 0 0
\(151\) 3.26795i 0.265942i −0.991120 0.132971i \(-0.957548\pi\)
0.991120 0.132971i \(-0.0424517\pi\)
\(152\) 1.09808 + 0.633975i 0.0890657 + 0.0514221i
\(153\) 1.96410 1.13397i 0.158788 0.0916764i
\(154\) 3.00000 1.73205i 0.241747 0.139573i
\(155\) 0 0
\(156\) −2.59808 2.50000i −0.208013 0.200160i
\(157\) 23.5885i 1.88256i 0.337622 + 0.941282i \(0.390378\pi\)
−0.337622 + 0.941282i \(0.609622\pi\)
\(158\) −4.73205 8.19615i −0.376462 0.652051i
\(159\) 0.232051 + 0.401924i 0.0184028 + 0.0318746i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 3.26795 5.66025i 0.255966 0.443345i −0.709192 0.705016i \(-0.750940\pi\)
0.965157 + 0.261670i \(0.0842733\pi\)
\(164\) 11.3923i 0.889590i
\(165\) 0 0
\(166\) 5.09808 + 8.83013i 0.395687 + 0.685351i
\(167\) −1.26795 2.19615i −0.0981169 0.169943i 0.812788 0.582559i \(-0.197949\pi\)
−0.910905 + 0.412616i \(0.864615\pi\)
\(168\) 0.732051i 0.0564789i
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 0 0
\(171\) 1.09808 0.633975i 0.0839720 0.0484812i
\(172\) −6.63397 + 3.83013i −0.505836 + 0.292044i
\(173\) −14.1962 8.19615i −1.07931 0.623142i −0.148602 0.988897i \(-0.547477\pi\)
−0.930711 + 0.365755i \(0.880811\pi\)
\(174\) 2.46410i 0.186803i
\(175\) 0 0
\(176\) 4.09808 + 2.36603i 0.308904 + 0.178346i
\(177\) −8.00000 −0.601317
\(178\) 2.19615 + 1.26795i 0.164609 + 0.0950368i
\(179\) −11.0263 19.0981i −0.824143 1.42746i −0.902573 0.430538i \(-0.858324\pi\)
0.0784298 0.996920i \(-0.475009\pi\)
\(180\) 0 0
\(181\) −8.80385 −0.654385 −0.327192 0.944958i \(-0.606103\pi\)
−0.327192 + 0.944958i \(0.606103\pi\)
\(182\) 1.83013 1.90192i 0.135658 0.140980i
\(183\) 1.19615i 0.0884221i
\(184\) 5.36603 3.09808i 0.395589 0.228393i
\(185\) 0 0
\(186\) −2.73205 + 4.73205i −0.200324 + 0.346971i
\(187\) −10.7321 −0.784805
\(188\) −4.09808 + 7.09808i −0.298883 + 0.517680i
\(189\) −0.633975 0.366025i −0.0461149 0.0266244i
\(190\) 0 0
\(191\) −3.46410 + 6.00000i −0.250654 + 0.434145i −0.963706 0.266966i \(-0.913979\pi\)
0.713052 + 0.701111i \(0.247312\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 4.13397 + 7.16025i 0.297570 + 0.515406i 0.975579 0.219647i \(-0.0704905\pi\)
−0.678009 + 0.735053i \(0.737157\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) −6.46410 −0.461722
\(197\) −4.92820 8.53590i −0.351120 0.608158i 0.635326 0.772244i \(-0.280866\pi\)
−0.986446 + 0.164086i \(0.947532\pi\)
\(198\) 4.09808 2.36603i 0.291238 0.168146i
\(199\) 1.90192 3.29423i 0.134824 0.233522i −0.790706 0.612196i \(-0.790286\pi\)
0.925530 + 0.378674i \(0.123620\pi\)
\(200\) 0 0
\(201\) 9.63397 + 5.56218i 0.679528 + 0.392326i
\(202\) −5.96410 + 10.3301i −0.419633 + 0.726825i
\(203\) 1.80385 0.126605
\(204\) −1.13397 + 1.96410i −0.0793941 + 0.137515i
\(205\) 0 0
\(206\) 16.2224 9.36603i 1.13027 0.652562i
\(207\) 6.19615i 0.430662i
\(208\) 3.50000 + 0.866025i 0.242681 + 0.0600481i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 2.19615 + 3.80385i 0.151189 + 0.261868i 0.931665 0.363319i \(-0.118356\pi\)
−0.780476 + 0.625186i \(0.785023\pi\)
\(212\) −0.401924 0.232051i −0.0276042 0.0159373i
\(213\) −1.26795 −0.0868784
\(214\) −0.169873 0.0980762i −0.0116123 0.00670435i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −3.46410 2.00000i −0.235159 0.135769i
\(218\) 4.73205 2.73205i 0.320495 0.185038i
\(219\) −8.42820 + 4.86603i −0.569525 + 0.328816i
\(220\) 0 0
\(221\) −7.85641 + 2.26795i −0.528479 + 0.152559i
\(222\) 10.4641i 0.702305i
\(223\) −6.53590 11.3205i −0.437676 0.758077i 0.559834 0.828605i \(-0.310865\pi\)
−0.997510 + 0.0705277i \(0.977532\pi\)
\(224\) 0.366025 + 0.633975i 0.0244561 + 0.0423592i
\(225\) 0 0
\(226\) 18.6603i 1.24126i
\(227\) 0.901924 1.56218i 0.0598628 0.103685i −0.834541 0.550946i \(-0.814267\pi\)
0.894404 + 0.447261i \(0.147600\pi\)
\(228\) −0.633975 + 1.09808i −0.0419860 + 0.0727219i
\(229\) 15.8564i 1.04782i 0.851773 + 0.523910i \(0.175527\pi\)
−0.851773 + 0.523910i \(0.824473\pi\)
\(230\) 0 0
\(231\) 1.73205 + 3.00000i 0.113961 + 0.197386i
\(232\) 1.23205 + 2.13397i 0.0808881 + 0.140102i
\(233\) 19.8564i 1.30084i −0.759576 0.650418i \(-0.774594\pi\)
0.759576 0.650418i \(-0.225406\pi\)
\(234\) 2.50000 2.59808i 0.163430 0.169842i
\(235\) 0 0
\(236\) 6.92820 4.00000i 0.450988 0.260378i
\(237\) 8.19615 4.73205i 0.532397 0.307380i
\(238\) −1.43782 0.830127i −0.0932002 0.0538091i
\(239\) 9.66025i 0.624870i 0.949939 + 0.312435i \(0.101145\pi\)
−0.949939 + 0.312435i \(0.898855\pi\)
\(240\) 0 0
\(241\) −15.2321 8.79423i −0.981183 0.566486i −0.0785557 0.996910i \(-0.525031\pi\)
−0.902627 + 0.430424i \(0.858364\pi\)
\(242\) −11.3923 −0.732325
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −0.598076 1.03590i −0.0382879 0.0663166i
\(245\) 0 0
\(246\) −11.3923 −0.726347
\(247\) −4.39230 + 1.26795i −0.279476 + 0.0806777i
\(248\) 5.46410i 0.346971i
\(249\) −8.83013 + 5.09808i −0.559587 + 0.323077i
\(250\) 0 0
\(251\) 3.26795 5.66025i 0.206271 0.357272i −0.744266 0.667883i \(-0.767200\pi\)
0.950537 + 0.310611i \(0.100534\pi\)
\(252\) 0.732051 0.0461149
\(253\) −14.6603 + 25.3923i −0.921682 + 1.59640i
\(254\) −15.4641 8.92820i −0.970304 0.560205i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 23.0885 13.3301i 1.44022 0.831510i 0.442355 0.896840i \(-0.354143\pi\)
0.997864 + 0.0653297i \(0.0208099\pi\)
\(258\) −3.83013 6.63397i −0.238453 0.413013i
\(259\) 7.66025 0.475985
\(260\) 0 0
\(261\) 2.46410 0.152524
\(262\) −6.73205 11.6603i −0.415907 0.720373i
\(263\) 24.2942 14.0263i 1.49805 0.864897i 0.498049 0.867149i \(-0.334050\pi\)
0.999997 + 0.00225153i \(0.000716686\pi\)
\(264\) −2.36603 + 4.09808i −0.145619 + 0.252219i
\(265\) 0 0
\(266\) −0.803848 0.464102i −0.0492871 0.0284559i
\(267\) −1.26795 + 2.19615i −0.0775972 + 0.134402i
\(268\) −11.1244 −0.679528
\(269\) −0.732051 + 1.26795i −0.0446339 + 0.0773082i −0.887479 0.460848i \(-0.847545\pi\)
0.842845 + 0.538156i \(0.180879\pi\)
\(270\) 0 0
\(271\) −5.07180 + 2.92820i −0.308090 + 0.177876i −0.646071 0.763277i \(-0.723589\pi\)
0.337982 + 0.941153i \(0.390256\pi\)
\(272\) 2.26795i 0.137515i
\(273\) 1.90192 + 1.83013i 0.115110 + 0.110764i
\(274\) 1.92820 0.116487
\(275\) 0 0
\(276\) 3.09808 + 5.36603i 0.186482 + 0.322997i
\(277\) 1.96410 + 1.13397i 0.118011 + 0.0681339i 0.557844 0.829946i \(-0.311629\pi\)
−0.439832 + 0.898080i \(0.644962\pi\)
\(278\) 9.85641 0.591148
\(279\) −4.73205 2.73205i −0.283300 0.163564i
\(280\) 0 0
\(281\) 22.3205i 1.33153i 0.746162 + 0.665765i \(0.231895\pi\)
−0.746162 + 0.665765i \(0.768105\pi\)
\(282\) −7.09808 4.09808i −0.422684 0.244037i
\(283\) −7.22243 + 4.16987i −0.429329 + 0.247873i −0.699061 0.715062i \(-0.746398\pi\)
0.269732 + 0.962936i \(0.413065\pi\)
\(284\) 1.09808 0.633975i 0.0651588 0.0376195i
\(285\) 0 0
\(286\) −16.3923 + 4.73205i −0.969297 + 0.279812i
\(287\) 8.33975i 0.492280i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −5.92820 10.2679i −0.348718 0.603997i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) 4.86603 8.42820i 0.284763 0.493223i
\(293\) 7.25833 12.5718i 0.424036 0.734452i −0.572294 0.820049i \(-0.693946\pi\)
0.996330 + 0.0855965i \(0.0272796\pi\)
\(294\) 6.46410i 0.376994i
\(295\) 0 0
\(296\) 5.23205 + 9.06218i 0.304107 + 0.526728i
\(297\) 2.36603 + 4.09808i 0.137291 + 0.237795i
\(298\) 2.80385i 0.162423i
\(299\) −5.36603 + 21.6865i −0.310325 + 1.25416i
\(300\) 0 0
\(301\) 4.85641 2.80385i 0.279919 0.161611i
\(302\) −2.83013 + 1.63397i −0.162856 + 0.0940247i
\(303\) −10.3301 5.96410i −0.593450 0.342629i
\(304\) 1.26795i 0.0727219i
\(305\) 0 0
\(306\) −1.96410 1.13397i −0.112280 0.0648250i
\(307\) −8.58846 −0.490169 −0.245085 0.969502i \(-0.578816\pi\)
−0.245085 + 0.969502i \(0.578816\pi\)
\(308\) −3.00000 1.73205i −0.170941 0.0986928i
\(309\) 9.36603 + 16.2224i 0.532815 + 0.922862i
\(310\) 0 0
\(311\) −15.6603 −0.888012 −0.444006 0.896024i \(-0.646443\pi\)
−0.444006 + 0.896024i \(0.646443\pi\)
\(312\) −0.866025 + 3.50000i −0.0490290 + 0.198148i
\(313\) 13.4641i 0.761036i 0.924774 + 0.380518i \(0.124254\pi\)
−0.924774 + 0.380518i \(0.875746\pi\)
\(314\) 20.4282 11.7942i 1.15283 0.665587i
\(315\) 0 0
\(316\) −4.73205 + 8.19615i −0.266199 + 0.461070i
\(317\) 3.33975 0.187579 0.0937894 0.995592i \(-0.470102\pi\)
0.0937894 + 0.995592i \(0.470102\pi\)
\(318\) 0.232051 0.401924i 0.0130128 0.0225388i
\(319\) −10.0981 5.83013i −0.565384 0.326424i
\(320\) 0 0
\(321\) 0.0980762 0.169873i 0.00547408 0.00948139i
\(322\) −3.92820 + 2.26795i −0.218910 + 0.126388i
\(323\) 1.43782 + 2.49038i 0.0800026 + 0.138569i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.53590 −0.361990
\(327\) 2.73205 + 4.73205i 0.151083 + 0.261683i
\(328\) 9.86603 5.69615i 0.544760 0.314517i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 0 0
\(331\) −17.3205 10.0000i −0.952021 0.549650i −0.0583130 0.998298i \(-0.518572\pi\)
−0.893708 + 0.448649i \(0.851905\pi\)
\(332\) 5.09808 8.83013i 0.279793 0.484616i
\(333\) 10.4641 0.573429
\(334\) −1.26795 + 2.19615i −0.0693791 + 0.120168i
\(335\) 0 0
\(336\) −0.633975 + 0.366025i −0.0345861 + 0.0199683i
\(337\) 6.85641i 0.373492i 0.982408 + 0.186746i \(0.0597942\pi\)
−0.982408 + 0.186746i \(0.940206\pi\)
\(338\) −11.0000 + 6.92820i −0.598321 + 0.376845i
\(339\) 18.6603 1.01349
\(340\) 0 0
\(341\) 12.9282 + 22.3923i 0.700101 + 1.21261i
\(342\) −1.09808 0.633975i −0.0593772 0.0342814i
\(343\) 9.85641 0.532196
\(344\) 6.63397 + 3.83013i 0.357680 + 0.206507i
\(345\) 0 0
\(346\) 16.3923i 0.881256i
\(347\) 7.68653 + 4.43782i 0.412635 + 0.238235i 0.691921 0.721973i \(-0.256765\pi\)
−0.279286 + 0.960208i \(0.590098\pi\)
\(348\) −2.13397 + 1.23205i −0.114393 + 0.0660449i
\(349\) −16.7321 + 9.66025i −0.895646 + 0.517102i −0.875785 0.482701i \(-0.839656\pi\)
−0.0198610 + 0.999803i \(0.506322\pi\)
\(350\) 0 0
\(351\) 2.59808 + 2.50000i 0.138675 + 0.133440i
\(352\) 4.73205i 0.252219i
\(353\) 9.89230 + 17.1340i 0.526514 + 0.911949i 0.999523 + 0.0308916i \(0.00983466\pi\)
−0.473008 + 0.881058i \(0.656832\pi\)
\(354\) 4.00000 + 6.92820i 0.212598 + 0.368230i
\(355\) 0 0
\(356\) 2.53590i 0.134402i
\(357\) 0.830127 1.43782i 0.0439350 0.0760976i
\(358\) −11.0263 + 19.0981i −0.582757 + 1.00936i
\(359\) 23.1244i 1.22046i 0.792226 + 0.610228i \(0.208922\pi\)
−0.792226 + 0.610228i \(0.791078\pi\)
\(360\) 0 0
\(361\) −8.69615 15.0622i −0.457692 0.792746i
\(362\) 4.40192 + 7.62436i 0.231360 + 0.400727i
\(363\) 11.3923i 0.597941i
\(364\) −2.56218 0.633975i −0.134295 0.0332293i
\(365\) 0 0
\(366\) 1.03590 0.598076i 0.0541473 0.0312619i
\(367\) 12.7583 7.36603i 0.665979 0.384503i −0.128572 0.991700i \(-0.541039\pi\)
0.794551 + 0.607197i \(0.207706\pi\)
\(368\) −5.36603 3.09808i −0.279723 0.161498i
\(369\) 11.3923i 0.593060i
\(370\) 0 0
\(371\) 0.294229 + 0.169873i 0.0152756 + 0.00881937i
\(372\) 5.46410 0.283300
\(373\) 8.89230 + 5.13397i 0.460426 + 0.265827i 0.712223 0.701953i \(-0.247688\pi\)
−0.251797 + 0.967780i \(0.581022\pi\)
\(374\) 5.36603 + 9.29423i 0.277471 + 0.480593i
\(375\) 0 0
\(376\) 8.19615 0.422684
\(377\) −8.62436 2.13397i −0.444177 0.109905i
\(378\) 0.732051i 0.0376526i
\(379\) −1.26795 + 0.732051i −0.0651302 + 0.0376029i −0.532211 0.846611i \(-0.678639\pi\)
0.467081 + 0.884214i \(0.345306\pi\)
\(380\) 0 0
\(381\) 8.92820 15.4641i 0.457406 0.792250i
\(382\) 6.92820 0.354478
\(383\) 2.73205 4.73205i 0.139601 0.241797i −0.787744 0.616002i \(-0.788751\pi\)
0.927346 + 0.374206i \(0.122085\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) 4.13397 7.16025i 0.210414 0.364447i
\(387\) 6.63397 3.83013i 0.337224 0.194696i
\(388\) 3.00000 + 5.19615i 0.152302 + 0.263795i
\(389\) −29.7846 −1.51014 −0.755070 0.655644i \(-0.772397\pi\)
−0.755070 + 0.655644i \(0.772397\pi\)
\(390\) 0 0
\(391\) 14.0526 0.710668
\(392\) 3.23205 + 5.59808i 0.163243 + 0.282746i
\(393\) 11.6603 6.73205i 0.588182 0.339587i
\(394\) −4.92820 + 8.53590i −0.248279 + 0.430032i
\(395\) 0 0
\(396\) −4.09808 2.36603i −0.205936 0.118897i
\(397\) −0.196152 + 0.339746i −0.00984461 + 0.0170514i −0.870906 0.491450i \(-0.836467\pi\)
0.861061 + 0.508501i \(0.169800\pi\)
\(398\) −3.80385 −0.190670
\(399\) 0.464102 0.803848i 0.0232341 0.0402427i
\(400\) 0 0
\(401\) −18.9904 + 10.9641i −0.948334 + 0.547521i −0.892563 0.450922i \(-0.851095\pi\)
−0.0557713 + 0.998444i \(0.517762\pi\)
\(402\) 11.1244i 0.554832i
\(403\) 14.1962 + 13.6603i 0.707161 + 0.680466i
\(404\) 11.9282 0.593450
\(405\) 0 0
\(406\) −0.901924 1.56218i −0.0447617 0.0775296i
\(407\) −42.8827 24.7583i −2.12562 1.22722i
\(408\) 2.26795 0.112280
\(409\) 12.3564 + 7.13397i 0.610985 + 0.352752i 0.773351 0.633978i \(-0.218579\pi\)
−0.162366 + 0.986731i \(0.551912\pi\)
\(410\) 0 0
\(411\) 1.92820i 0.0951113i
\(412\) −16.2224 9.36603i −0.799222 0.461431i
\(413\) −5.07180 + 2.92820i −0.249567 + 0.144087i
\(414\) −5.36603 + 3.09808i −0.263726 + 0.152262i
\(415\) 0 0
\(416\) −1.00000 3.46410i −0.0490290 0.169842i
\(417\) 9.85641i 0.482670i
\(418\) 3.00000 + 5.19615i 0.146735 + 0.254152i
\(419\) −5.26795 9.12436i −0.257356 0.445754i 0.708177 0.706035i \(-0.249518\pi\)
−0.965533 + 0.260281i \(0.916185\pi\)
\(420\) 0 0
\(421\) 32.7128i 1.59432i 0.603765 + 0.797162i \(0.293667\pi\)
−0.603765 + 0.797162i \(0.706333\pi\)
\(422\) 2.19615 3.80385i 0.106907 0.185168i
\(423\) 4.09808 7.09808i 0.199255 0.345120i
\(424\) 0.464102i 0.0225388i
\(425\) 0 0
\(426\) 0.633975 + 1.09808i 0.0307162 + 0.0532020i
\(427\) 0.437822 + 0.758330i 0.0211877 + 0.0366982i
\(428\) 0.196152i 0.00948139i
\(429\) −4.73205 16.3923i −0.228466 0.791428i
\(430\) 0 0
\(431\) −9.63397 + 5.56218i −0.464052 + 0.267921i −0.713747 0.700404i \(-0.753003\pi\)
0.249694 + 0.968325i \(0.419670\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) −12.8660 7.42820i −0.618302 0.356977i 0.157906 0.987454i \(-0.449526\pi\)
−0.776208 + 0.630478i \(0.782859\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 0 0
\(436\) −4.73205 2.73205i −0.226624 0.130842i
\(437\) 7.85641 0.375823
\(438\) 8.42820 + 4.86603i 0.402715 + 0.232508i
\(439\) 8.83013 + 15.2942i 0.421439 + 0.729954i 0.996080 0.0884515i \(-0.0281918\pi\)
−0.574642 + 0.818405i \(0.694859\pi\)
\(440\) 0 0
\(441\) 6.46410 0.307814
\(442\) 5.89230 + 5.66987i 0.280268 + 0.269688i
\(443\) 36.3923i 1.72905i 0.502589 + 0.864525i \(0.332381\pi\)
−0.502589 + 0.864525i \(0.667619\pi\)
\(444\) −9.06218 + 5.23205i −0.430072 + 0.248302i
\(445\) 0 0
\(446\) −6.53590 + 11.3205i −0.309484 + 0.536042i
\(447\) 2.80385 0.132617
\(448\) 0.366025 0.633975i 0.0172931 0.0299525i
\(449\) 20.1962 + 11.6603i 0.953115 + 0.550281i 0.894047 0.447973i \(-0.147854\pi\)
0.0590680 + 0.998254i \(0.481187\pi\)
\(450\) 0 0
\(451\) −26.9545 + 46.6865i −1.26924 + 2.19838i
\(452\) −16.1603 + 9.33013i −0.760114 + 0.438852i
\(453\) −1.63397 2.83013i −0.0767708 0.132971i
\(454\) −1.80385 −0.0846588
\(455\) 0 0
\(456\) 1.26795 0.0593772
\(457\) −9.33013 16.1603i −0.436445 0.755945i 0.560967 0.827838i \(-0.310429\pi\)
−0.997412 + 0.0718931i \(0.977096\pi\)
\(458\) 13.7321 7.92820i 0.641657 0.370461i
\(459\) 1.13397 1.96410i 0.0529294 0.0916764i
\(460\) 0 0
\(461\) −22.2846 12.8660i −1.03790 0.599231i −0.118661 0.992935i \(-0.537860\pi\)
−0.919237 + 0.393704i \(0.871193\pi\)
\(462\) 1.73205 3.00000i 0.0805823 0.139573i
\(463\) −28.0526 −1.30371 −0.651856 0.758342i \(-0.726010\pi\)
−0.651856 + 0.758342i \(0.726010\pi\)
\(464\) 1.23205 2.13397i 0.0571965 0.0990673i
\(465\) 0 0
\(466\) −17.1962 + 9.92820i −0.796596 + 0.459915i
\(467\) 12.5885i 0.582524i −0.956643 0.291262i \(-0.905925\pi\)
0.956643 0.291262i \(-0.0940752\pi\)
\(468\) −3.50000 0.866025i −0.161788 0.0400320i
\(469\) 8.14359 0.376036
\(470\) 0 0
\(471\) 11.7942 + 20.4282i 0.543449 + 0.941282i
\(472\) −6.92820 4.00000i −0.318896 0.184115i
\(473\) −36.2487 −1.66672
\(474\) −8.19615 4.73205i −0.376462 0.217350i
\(475\) 0 0
\(476\) 1.66025i 0.0760976i
\(477\) 0.401924 + 0.232051i 0.0184028 + 0.0106249i
\(478\) 8.36603 4.83013i 0.382653 0.220925i
\(479\) 22.9808 13.2679i 1.05002 0.606228i 0.127363 0.991856i \(-0.459349\pi\)
0.922654 + 0.385628i \(0.126015\pi\)
\(480\) 0 0
\(481\) −36.6244 9.06218i −1.66993 0.413200i
\(482\) 17.5885i 0.801132i
\(483\) −2.26795 3.92820i −0.103195 0.178739i
\(484\) 5.69615 + 9.86603i 0.258916 + 0.448456i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −10.5622 + 18.2942i −0.478618 + 0.828991i −0.999699 0.0245163i \(-0.992195\pi\)
0.521081 + 0.853507i \(0.325529\pi\)
\(488\) −0.598076 + 1.03590i −0.0270736 + 0.0468929i
\(489\) 6.53590i 0.295564i
\(490\) 0 0
\(491\) 2.63397 + 4.56218i 0.118870 + 0.205888i 0.919320 0.393511i \(-0.128740\pi\)
−0.800450 + 0.599399i \(0.795406\pi\)
\(492\) 5.69615 + 9.86603i 0.256802 + 0.444795i
\(493\) 5.58846i 0.251691i
\(494\) 3.29423 + 3.16987i 0.148214 + 0.142619i
\(495\) 0 0
\(496\) −4.73205 + 2.73205i −0.212475 + 0.122673i
\(497\) −0.803848 + 0.464102i −0.0360575 + 0.0208178i
\(498\) 8.83013 + 5.09808i 0.395687 + 0.228450i
\(499\) 32.0000i 1.43252i −0.697835 0.716258i \(-0.745853\pi\)
0.697835 0.716258i \(-0.254147\pi\)
\(500\) 0 0
\(501\) −2.19615 1.26795i −0.0981169 0.0566478i
\(502\) −6.53590 −0.291711
\(503\) 9.50962 + 5.49038i 0.424013 + 0.244804i 0.696793 0.717272i \(-0.254610\pi\)
−0.272780 + 0.962076i \(0.587943\pi\)
\(504\) −0.366025 0.633975i −0.0163041 0.0282395i
\(505\) 0 0
\(506\) 29.3205 1.30346
\(507\) −6.92820 11.0000i −0.307692 0.488527i
\(508\) 17.8564i 0.792250i
\(509\) −8.89230 + 5.13397i −0.394144 + 0.227559i −0.683954 0.729525i \(-0.739741\pi\)
0.289810 + 0.957084i \(0.406408\pi\)
\(510\) 0 0
\(511\) −3.56218 + 6.16987i −0.157581 + 0.272939i
\(512\) 1.00000 0.0441942
\(513\) 0.633975 1.09808i 0.0279907 0.0484812i
\(514\) −23.0885 13.3301i −1.01839 0.587967i
\(515\) 0 0
\(516\) −3.83013 + 6.63397i −0.168612 + 0.292044i
\(517\) −33.5885 + 19.3923i −1.47722 + 0.852873i
\(518\) −3.83013 6.63397i −0.168286 0.291480i
\(519\) −16.3923 −0.719542
\(520\) 0 0
\(521\) −17.4449 −0.764273 −0.382137 0.924106i \(-0.624812\pi\)
−0.382137 + 0.924106i \(0.624812\pi\)
\(522\) −1.23205 2.13397i −0.0539254 0.0934015i
\(523\) 31.5622 18.2224i 1.38012 0.796811i 0.387945 0.921683i \(-0.373185\pi\)
0.992173 + 0.124871i \(0.0398518\pi\)
\(524\) −6.73205 + 11.6603i −0.294091 + 0.509381i
\(525\) 0 0
\(526\) −24.2942 14.0263i −1.05928 0.611575i
\(527\) 6.19615 10.7321i 0.269909 0.467495i
\(528\) 4.73205 0.205936
\(529\) 7.69615 13.3301i 0.334615 0.579571i
\(530\) 0 0
\(531\) −6.92820 + 4.00000i −0.300658 + 0.173585i
\(532\) 0.928203i 0.0402427i
\(533\) −9.86603 + 39.8731i −0.427345 + 1.72709i
\(534\) 2.53590 0.109739
\(535\) 0 0
\(536\) 5.56218 + 9.63397i 0.240249 + 0.416124i
\(537\) −19.0981 11.0263i −0.824143 0.475819i
\(538\) 1.46410 0.0631219
\(539\) −26.4904 15.2942i −1.14102 0.658769i
\(540\) 0 0
\(541\) 40.3205i 1.73351i −0.498731 0.866757i \(-0.666200\pi\)
0.498731 0.866757i \(-0.333800\pi\)
\(542\) 5.07180 + 2.92820i 0.217852 + 0.125777i
\(543\) −7.62436 + 4.40192i −0.327192 + 0.188905i
\(544\) −1.96410 + 1.13397i −0.0842102 + 0.0486188i
\(545\) 0 0
\(546\) 0.633975 2.56218i 0.0271316 0.109651i
\(547\) 6.19615i 0.264928i −0.991188 0.132464i \(-0.957711\pi\)
0.991188 0.132464i \(-0.0422889\pi\)
\(548\) −0.964102 1.66987i −0.0411844 0.0713334i
\(549\) 0.598076 + 1.03590i 0.0255253 + 0.0442111i
\(550\) 0 0
\(551\) 3.12436i 0.133102i
\(552\) 3.09808 5.36603i 0.131863 0.228393i
\(553\) 3.46410 6.00000i 0.147309 0.255146i
\(554\) 2.26795i 0.0963559i
\(555\) 0 0
\(556\) −4.92820 8.53590i −0.209002 0.362003i
\(557\) −15.1865 26.3038i −0.643474 1.11453i −0.984652 0.174531i \(-0.944159\pi\)
0.341178 0.939999i \(-0.389174\pi\)
\(558\) 5.46410i 0.231314i
\(559\) −26.5359 + 7.66025i −1.12235 + 0.323994i
\(560\) 0 0
\(561\) −9.29423 + 5.36603i −0.392403 + 0.226554i
\(562\) 19.3301 11.1603i 0.815392 0.470767i
\(563\) 18.2487 + 10.5359i 0.769091 + 0.444035i 0.832550 0.553949i \(-0.186880\pi\)
−0.0634589 + 0.997984i \(0.520213\pi\)
\(564\) 8.19615i 0.345120i
\(565\) 0 0
\(566\) 7.22243 + 4.16987i 0.303581 + 0.175273i
\(567\) −0.732051 −0.0307432
\(568\) −1.09808 0.633975i −0.0460743 0.0266010i
\(569\) 19.3205 + 33.4641i 0.809958 + 1.40289i 0.912893 + 0.408200i \(0.133843\pi\)
−0.102935 + 0.994688i \(0.532823\pi\)
\(570\) 0 0
\(571\) 24.0526 1.00657 0.503284 0.864121i \(-0.332125\pi\)
0.503284 + 0.864121i \(0.332125\pi\)
\(572\) 12.2942 + 11.8301i 0.514048 + 0.494642i
\(573\) 6.92820i 0.289430i
\(574\) −7.22243 + 4.16987i −0.301458 + 0.174047i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 0.267949 0.0111549 0.00557744 0.999984i \(-0.498225\pi\)
0.00557744 + 0.999984i \(0.498225\pi\)
\(578\) −5.92820 + 10.2679i −0.246581 + 0.427090i
\(579\) 7.16025 + 4.13397i 0.297570 + 0.171802i
\(580\) 0 0
\(581\) −3.73205 + 6.46410i −0.154832 + 0.268176i
\(582\) −5.19615 + 3.00000i −0.215387 + 0.124354i
\(583\) −1.09808 1.90192i −0.0454777 0.0787696i
\(584\) −9.73205 −0.402715
\(585\) 0 0
\(586\) −14.5167 −0.599678
\(587\) −8.00000 13.8564i −0.330195 0.571915i 0.652355 0.757914i \(-0.273781\pi\)
−0.982550 + 0.185999i \(0.940448\pi\)
\(588\) −5.59808 + 3.23205i −0.230861 + 0.133288i
\(589\) 3.46410 6.00000i 0.142736 0.247226i
\(590\) 0 0
\(591\) −8.53590 4.92820i −0.351120 0.202719i
\(592\) 5.23205 9.06218i 0.215036 0.372453i
\(593\) −36.8564 −1.51351 −0.756756 0.653698i \(-0.773217\pi\)
−0.756756 + 0.653698i \(0.773217\pi\)
\(594\) 2.36603 4.09808i 0.0970792 0.168146i
\(595\) 0 0
\(596\) −2.42820 + 1.40192i −0.0994631 + 0.0574250i
\(597\) 3.80385i 0.155681i
\(598\) 21.4641 6.19615i 0.877732 0.253380i
\(599\) 9.46410 0.386693 0.193346 0.981131i \(-0.438066\pi\)
0.193346 + 0.981131i \(0.438066\pi\)
\(600\) 0 0
\(601\) 2.96410 + 5.13397i 0.120908 + 0.209419i 0.920126 0.391622i \(-0.128086\pi\)
−0.799218 + 0.601041i \(0.794753\pi\)
\(602\) −4.85641 2.80385i −0.197932 0.114276i
\(603\) 11.1244 0.453019
\(604\) 2.83013 + 1.63397i 0.115156 + 0.0664855i
\(605\) 0 0
\(606\) 11.9282i 0.484550i
\(607\) 0.679492 + 0.392305i 0.0275797 + 0.0159232i 0.513726 0.857954i \(-0.328265\pi\)
−0.486147 + 0.873877i \(0.661598\pi\)
\(608\) −1.09808 + 0.633975i −0.0445329 + 0.0257111i
\(609\) 1.56218 0.901924i 0.0633026 0.0365478i
\(610\) 0 0
\(611\) −20.4904 + 21.2942i −0.828952 + 0.861472i
\(612\) 2.26795i 0.0916764i
\(613\) 5.69615 + 9.86603i 0.230065 + 0.398485i 0.957827 0.287345i \(-0.0927726\pi\)
−0.727762 + 0.685830i \(0.759439\pi\)
\(614\) 4.29423 + 7.43782i 0.173301 + 0.300166i
\(615\) 0 0
\(616\) 3.46410i 0.139573i
\(617\) −17.6244 + 30.5263i −0.709530 + 1.22894i 0.255502 + 0.966809i \(0.417759\pi\)
−0.965032 + 0.262133i \(0.915574\pi\)
\(618\) 9.36603 16.2224i 0.376757 0.652562i
\(619\) 10.5359i 0.423474i 0.977327 + 0.211737i \(0.0679119\pi\)
−0.977327 + 0.211737i \(0.932088\pi\)
\(620\) 0 0
\(621\) −3.09808 5.36603i −0.124322 0.215331i
\(622\) 7.83013 + 13.5622i 0.313959 + 0.543794i
\(623\) 1.85641i 0.0743754i
\(624\) 3.46410 1.00000i 0.138675 0.0400320i
\(625\) 0 0
\(626\) 11.6603 6.73205i 0.466037 0.269067i
\(627\) −5.19615 + 3.00000i −0.207514 + 0.119808i
\(628\) −20.4282 11.7942i −0.815174 0.470641i
\(629\) 23.7321i 0.946259i
\(630\) 0 0
\(631\) 41.3205 + 23.8564i 1.64494 + 0.949709i 0.979039 + 0.203671i \(0.0652874\pi\)
0.665904 + 0.746037i \(0.268046\pi\)
\(632\) 9.46410 0.376462
\(633\) 3.80385 + 2.19615i 0.151189 + 0.0872892i
\(634\) −1.66987 2.89230i −0.0663191 0.114868i
\(635\) 0 0
\(636\) −0.464102 −0.0184028
\(637\) −22.6244 5.59808i −0.896410 0.221804i
\(638\) 11.6603i 0.461634i
\(639\) −1.09808 + 0.633975i −0.0434392 + 0.0250796i
\(640\) 0 0
\(641\) 12.9904 22.5000i 0.513089 0.888697i −0.486796 0.873516i \(-0.661834\pi\)
0.999885 0.0151806i \(-0.00483233\pi\)
\(642\) −0.196152 −0.00774152
\(643\) 6.92820 12.0000i 0.273222 0.473234i −0.696463 0.717592i \(-0.745244\pi\)
0.969685 + 0.244359i \(0.0785774\pi\)
\(644\) 3.92820 + 2.26795i 0.154793 + 0.0893697i
\(645\) 0 0
\(646\) 1.43782 2.49038i 0.0565704 0.0979827i
\(647\) 22.7321 13.1244i 0.893689 0.515972i 0.0185417 0.999828i \(-0.494098\pi\)
0.875147 + 0.483856i \(0.160764\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 37.8564 1.48599
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) 3.26795 + 5.66025i 0.127983 + 0.221673i
\(653\) −9.12436 + 5.26795i −0.357064 + 0.206151i −0.667792 0.744348i \(-0.732760\pi\)
0.310728 + 0.950499i \(0.399427\pi\)
\(654\) 2.73205 4.73205i 0.106832 0.185038i
\(655\) 0 0
\(656\) −9.86603 5.69615i −0.385204 0.222397i
\(657\) −4.86603 + 8.42820i −0.189842 + 0.328816i
\(658\) −6.00000 −0.233904
\(659\) 19.1244 33.1244i 0.744979 1.29034i −0.205225 0.978715i \(-0.565793\pi\)
0.950205 0.311627i \(-0.100874\pi\)
\(660\) 0 0
\(661\) 8.13397 4.69615i 0.316375 0.182659i −0.333401 0.942785i \(-0.608196\pi\)
0.649776 + 0.760126i \(0.274863\pi\)
\(662\) 20.0000i 0.777322i
\(663\) −5.66987 + 5.89230i −0.220200 + 0.228838i
\(664\) −10.1962 −0.395687
\(665\) 0 0
\(666\) −5.23205 9.06218i −0.202738 0.351152i
\(667\) 13.2224 + 7.63397i 0.511975 + 0.295589i
\(668\) 2.53590 0.0981169
\(669\) −11.3205 6.53590i −0.437676 0.252692i
\(670\) 0 0
\(671\) 5.66025i 0.218512i
\(672\) 0.633975 + 0.366025i 0.0244561 + 0.0141197i
\(673\) −12.1865 + 7.03590i −0.469756 + 0.271214i −0.716138 0.697959i \(-0.754092\pi\)
0.246381 + 0.969173i \(0.420758\pi\)
\(674\) 5.93782 3.42820i 0.228716 0.132049i
\(675\) 0 0
\(676\) 11.5000 + 6.06218i 0.442308 + 0.233161i
\(677\) 38.5359i 1.48105i 0.672026 + 0.740527i \(0.265424\pi\)
−0.672026 + 0.740527i \(0.734576\pi\)
\(678\) −9.33013 16.1603i −0.358321 0.620631i
\(679\) −2.19615 3.80385i −0.0842806 0.145978i
\(680\) 0 0
\(681\) 1.80385i 0.0691236i
\(682\) 12.9282 22.3923i 0.495046 0.857446i
\(683\) 18.9282 32.7846i 0.724268 1.25447i −0.235007 0.971994i \(-0.575511\pi\)
0.959275 0.282475i \(-0.0911553\pi\)
\(684\) 1.26795i 0.0484812i
\(685\) 0 0
\(686\) −4.92820 8.53590i −0.188160 0.325902i
\(687\) 7.92820 + 13.7321i 0.302480 + 0.523910i
\(688\) 7.66025i 0.292044i
\(689\) −1.20577 1.16025i −0.0459362 0.0442022i
\(690\) 0 0
\(691\) 22.8109 13.1699i 0.867767 0.501006i 0.00116153 0.999999i \(-0.499630\pi\)
0.866606 + 0.498994i \(0.166297\pi\)
\(692\) 14.1962 8.19615i 0.539657 0.311571i
\(693\) 3.00000 + 1.73205i 0.113961 + 0.0657952i
\(694\) 8.87564i 0.336915i
\(695\) 0 0
\(696\) 2.13397 + 1.23205i 0.0808881 + 0.0467008i
\(697\) 25.8372 0.978653
\(698\) 16.7321 + 9.66025i 0.633317 + 0.365646i
\(699\) −9.92820 17.1962i −0.375519 0.650418i
\(700\) 0 0
\(701\) −31.3205 −1.18296 −0.591480 0.806320i \(-0.701456\pi\)
−0.591480 + 0.806320i \(0.701456\pi\)
\(702\) 0.866025 3.50000i 0.0326860 0.132099i
\(703\) 13.2679i 0.500410i
\(704\) −4.09808 + 2.36603i −0.154452 + 0.0891729i
\(705\) 0 0
\(706\) 9.89230 17.1340i 0.372302 0.644846i
\(707\) −8.73205 −0.328403
\(708\) 4.00000 6.92820i 0.150329 0.260378i
\(709\) −35.3827 20.4282i −1.32882 0.767197i −0.343707 0.939077i \(-0.611683\pi\)
−0.985118 + 0.171880i \(0.945016\pi\)
\(710\) 0 0
\(711\) 4.73205 8.19615i 0.177466 0.307380i
\(712\) −2.19615 + 1.26795i −0.0823043 + 0.0475184i
\(713\) −16.9282 29.3205i −0.633966 1.09806i
\(714\) −1.66025 −0.0621334
\(715\) 0 0
\(716\) 22.0526 0.824143
\(717\) 4.83013 + 8.36603i 0.180384 + 0.312435i
\(718\) 20.0263 11.5622i 0.747374 0.431497i
\(719\) 11.2679 19.5167i 0.420224 0.727849i −0.575737 0.817635i \(-0.695285\pi\)
0.995961 + 0.0897860i \(0.0286183\pi\)
\(720\) 0 0
\(721\) 11.8756 + 6.85641i 0.442272 + 0.255346i
\(722\) −8.69615 + 15.0622i −0.323637 + 0.560556i
\(723\) −17.5885 −0.654122
\(724\) 4.40192 7.62436i 0.163596 0.283357i
\(725\) 0 0
\(726\) −9.86603 + 5.69615i −0.366163 + 0.211404i
\(727\) 20.9808i 0.778133i 0.921210 + 0.389067i \(0.127202\pi\)
−0.921210 + 0.389067i \(0.872798\pi\)
\(728\) 0.732051 + 2.53590i 0.0271316 + 0.0939866i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 8.68653 + 15.0455i 0.321283 + 0.556479i
\(732\) −1.03590 0.598076i −0.0382879 0.0221055i
\(733\) −19.0000 −0.701781 −0.350891 0.936416i \(-0.614121\pi\)
−0.350891 + 0.936416i \(0.614121\pi\)
\(734\) −12.7583 7.36603i −0.470919 0.271885i
\(735\) 0 0
\(736\) 6.19615i 0.228393i
\(737\) −45.5885 26.3205i −1.67927 0.969528i
\(738\) −9.86603 + 5.69615i −0.363173 + 0.209678i
\(739\) −9.46410 + 5.46410i −0.348143 + 0.201000i −0.663867 0.747851i \(-0.731086\pi\)
0.315724 + 0.948851i \(0.397753\pi\)
\(740\) 0 0
\(741\) −3.16987 + 3.29423i −0.116448 + 0.121017i
\(742\) 0.339746i 0.0124725i
\(743\) −13.8038 23.9090i −0.506414 0.877135i −0.999972 0.00742221i \(-0.997637\pi\)
0.493558 0.869713i \(-0.335696\pi\)
\(744\) −2.73205 4.73205i −0.100162 0.173485i
\(745\) 0 0
\(746\) 10.2679i 0.375936i
\(747\) −5.09808 + 8.83013i −0.186529 + 0.323077i
\(748\) 5.36603 9.29423i 0.196201 0.339831i
\(749\) 0.143594i 0.00524679i
\(750\) 0 0
\(751\) 7.95448 + 13.7776i 0.290263 + 0.502751i 0.973872 0.227098i \(-0.0729238\pi\)
−0.683609 + 0.729849i \(0.739590\pi\)
\(752\) −4.09808 7.09808i −0.149441 0.258840i
\(753\) 6.53590i 0.238181i
\(754\) 2.46410 + 8.53590i 0.0897373 + 0.310859i
\(755\) 0 0
\(756\) 0.633975 0.366025i 0.0230574 0.0133122i
\(757\) −6.12436 + 3.53590i −0.222593 + 0.128514i −0.607151 0.794587i \(-0.707688\pi\)
0.384557 + 0.923101i \(0.374354\pi\)
\(758\) 1.26795 + 0.732051i 0.0460540 + 0.0265893i
\(759\) 29.3205i 1.06427i
\(760\) 0 0
\(761\) −20.1962 11.6603i −0.732110 0.422684i 0.0870836 0.996201i \(-0.472245\pi\)
−0.819194 + 0.573517i \(0.805579\pi\)
\(762\) −17.8564 −0.646869
\(763\) 3.46410 + 2.00000i 0.125409 + 0.0724049i
\(764\) −3.46410 6.00000i −0.125327 0.217072i
\(765\) 0 0
\(766\) −5.46410 −0.197426
\(767\) 27.7128 8.00000i 1.00065 0.288863i
\(768\) 1.00000i 0.0360844i
\(769\) 13.9808 8.07180i 0.504159 0.291076i −0.226270 0.974065i \(-0.572653\pi\)
0.730429 + 0.682988i \(0.239320\pi\)
\(770\) 0 0
\(771\) 13.3301 23.0885i 0.480073 0.831510i
\(772\) −8.26795 −0.297570
\(773\) −17.5359 + 30.3731i −0.630722 + 1.09244i 0.356682 + 0.934226i \(0.383908\pi\)
−0.987404 + 0.158217i \(0.949425\pi\)
\(774\) −6.63397 3.83013i −0.238453 0.137671i
\(775\) 0 0
\(776\) 3.00000 5.19615i 0.107694 0.186531i
\(777\) 6.63397 3.83013i 0.237993 0.137405i
\(778\) 14.8923 + 25.7942i 0.533915 + 0.924768i
\(779\) 14.4449 0.517541
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) −7.02628 12.1699i −0.251259 0.435194i
\(783\) 2.13397 1.23205i 0.0762620 0.0440299i